Concept 12.2
Volume of a Combined Solid
Source: NCERT Mathematics, Class 108 minute lesson
Formal statement
The volume of a solid made by joining two solids is the sum of their volumes.
The intuition
Volume is the amount of space filled. Joining two solids doesn't create or destroy any space, so volumes just add.
This is the opposite of surface area, where joining hides faces. Fill one part with water, then the other: the total is the sum.
The attention
Look at the volumes as pieces of space: they simply add.
Volume = V(cone) + V(hemisphere) nothing to remove, unlike surface area
Look hereNot here
- Look here
- The volumes, simply added. Joining two solids doesn't overlap them, so no space is counted twice.
- Not here
- Thinking in surface areas. Subtracting the joined face mixes ideas: a face is an area and has no volume.
- What it teaches
- Different quantities combine by different rules. Ask what the quantity measures.